Laser beam and electron beams have been used to produce fusion reactions involving heavy isotopes of hydrogen. This method suffers from a number of drawbacks which the method using ion beams seeks to obviate. Among these disadvantages are: the beams of the prior art do fail to carry energetic nuclear reactants in to the reaction zone; the nuclear reaction rely on thermal heating rather than on an accelerated ion beam reaction mechanism; the prior art experiences severe difficulties in the attempts to correlate the acceleration, focusing, synchronizing of all beams. The apparatus and the method of the present invention seek to overcome the above listed drawbacks of prior art.